Average Cost Function

Business Calculus · Axiom Academy

Understanding cost per unit and its relationship to marginal cost While marginal cost tells us about the next unit, average cost tells us the cost per unit across all production. The average cost function (or unit cost) is total cost divided by quantity: Average Cost = Total Cost ÷ Quantity Example: Manufacturing Company A company has total cost function: Find the average cost function: Notice the term x . As x increases, this term decreases! This is why average cost typically drops as you produce more - fixed costs are spread over more units. Let's evaluate at different quantities: The average cost curve has a distinctive U-shape: At low production: AC is high because fixed costs are spread over few units At minimum AC: This is the most efficient production level At high production: AC rises due to diminishing returns There's a powerful relationship between average cost and marginal cost: MC crosses AC at the minimum of AC When AC is at its minimum, MC = AC. When MC Adding a cheaper unit pulls the average down When MC > AC: Adding a more expensive unit pulls the average up When MC = AC: Adding a unit at the average doesn't change the average The minimum average cost point is called the efficient scale - it's the production level where the company achieves the lowest cost per unit. If C(x) = 1000 + 5x , what is the average cost function? At the minimum point of the average cost curve, which statement is true? You understand average cost and its relationship to marginal cost!

This is the written version of the interactive lesson above. See the full Business Calculus course.